Meriam, Kraige & Bolton — Statics of Particles: Problem 2_113

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/113 The turnbuckle is tightened until the tension in cable AB is 1.2 kN. Calculate the magnitude of the moment about point O of the force acting on point A. Problem 2/113 ● Step 1: Identify Coordinates and Position Vectors Based on the provided diagram, we establish a coordinate system with the origin at point . The coordinates of the relevant points are determined from the given dimensions (all in meters): Origin: Point (end of the horizontal arm at the top of the post): Point (cable attachment point on the ground): The position vector from the origin to the point of force application is: ● Step 2: Define the Tension Force Vector The tension force acts on point and is directed toward point . We first find the displacement vector : The magnitude (length) of the cable segment is: Given the tension magnitude , the force vector is expressed as: ● Step 3: Calculate the Moment about Point O The moment vector is defined by the cross product : O(0,0,0) O=(0,0,0) AA=(1.6,0,2) BB=(1.5,0.8,0) OA r = OA 1.6i+2k m TAB AB = ABr − B r = A (1.5−1.6)i+(0.8−0)j+(0−2)k=−0.1i+0.8j−2 AB L = AB = (−0.1)+0.8+(−2) 222 = 0.01+0.64+4 ≈ 4.652.1564 T=1.2 kN T=T = L AB AB (−0.1i+ 4.65 1.2 0.8j−2k) kN M O r × OA T Factoring out the scalar constant and performing the cross product: ● Step 4: Determine the Magnitude of the Moment 1. Present Final Formula: 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The magnitude of t